CONSTRUCTION OF HADAMARD MATRICES FROM CERTAIN FROBENIUS GROUP

Abstract

Hadamard matrices have many application in computer science and communication technology. It is shown that two classical methods of constructing Hadamard matrices viz., those of Paley’s and Williamson’s can be unified and Paley’s and Williamson’s Hadamard matrices can be constructed by a uniform method i.e. producing an association scheme or coherent configuration by Frobenius group action and then producing Hadamard matrices by taking suitable (1-1) -linear combinations of adjacency matrices of the coherent configuration.

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March 10, 2026

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